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Some coarsely chopped pitted olives would work. Ideally green (not stuffed with pimientos). Good black olives could work but not the tinned ones, they're too bland. Pickled onions, finely chopped, would also work. Just something to give the dish a little bite. You could get away without them but just be sure you're squeezing in some fresh lemon juice and maybe a teaspoon or two of freshly-grated lemon rind.

Yes, I love Peggeen's suggestion of chopped olives, and I'm guessing that she implies green. Quick-pickled onions would be lovely, too. I have made these often enough that I keep them on hand always (I am a vegetarian, but the pickled onions are the icing on any proverbial cake) : http://food52.com/recipes...

I was thinking olives, too, or chopped sun dried tomatoes. Or even anchovies (my favorite).
Or you can go in another direction; some kind of dried fruit like currants, apricots, or raisins (great with chicken).

ChefJune I was about to ask the same thing. Capers don't need to be briney, in fact I vastly prefer the salt packed ones, although you do need to rinse the salt off. Using olives as a substitute I like cerignola or luques. You don't even need to pit them just let your guests know that olives have pits.

Karen, your chicken piccata dinner may have already come and gone... but in case you're still toying with ideas, I liked PazzoNico's suggestion to combine salt and sweet. Green pitted olives, some (golden) raisins and maybe sun-dried tomatoes. Garlic slivers. Lemon juice and maybe some tiny chunks of lemon pith.
Hope you have a great dinner!

Thank you for all your helpful answers!! I did not have capers on hand, so took your advice and used green olives instead and it came out great!!! My boyfriend loved it! Thanks again for all your help!